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Cost of Capital


Cost of Capital & Risk Analysis MBA Fellows Corporate Finance Learning Module Part II Class Topics Incorporating risk in Capital Budgeting Cost of Capital Components ... – PowerPoint PPT presentation

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Title: Cost of Capital

Cost of Capital Risk Analysis
  • MBA Fellows
  • Corporate Finance Learning Module
  • Part II

Class Topics
  • Incorporating risk in Capital Budgeting
  • Cost of Capital Components cost of debt,
    preferred stock, common equity.
  • Calculating the Weighted Average Cost of Capital
  • Capital Structure Decisions
  • EVA

Capital Budgeting and Risk
  • Prior discussion of alternative projects assumed
    that the level of risk associated with each
    project was the same.
  • How do you evaluate projects when they have
    different levels of risk?

Project Risk
  • Reflects the the potential variability of
  • Portfolio effect - if a projects proposed
    returns are not perfectly correlated with the
    returns from the firms other projects.
  • Diversification - influences risk. The total
    risk of the firm may be reduced by accepting the
    proposed project, if its returns are not
    perfectly correlated with the returns from the
    firms other investments.

Types of Project Risk
  • Stand-alone Risk
  • Corporate/Within Firm Risk
  • Market/Beta Risk
  • All Risk is not equal - some risk can be
    diversified away, and some cannot.

Stand-Alone Risk
  • The risk associated with a particular project,
    ignoring the firms other projects/assets and
    firm/shareholder diversification.
  • Measured by the ? (standard deviation) or CV
    (coefficient of variation) of NPV, IRR, or MIRR.
  • Methods for estimating stand-alone risk
    Sensitivity Analysis, Scenario Analysis, Monte
    Carlo Simulation

Stand-alone risk
  • Stand-alone risk is easiest to measure, more
  • Core projects are highly correlated with other
    assets, so stand-alone risk generally reflects
    corporate risk.
  • If the project is highly correlated with the
    economy, stand-alone risk also reflects market

Coefficient of Variation (COV)
  • COV is a relative measure of stand-alone risk
    used. It used to compare the risk of 2 or more
    assets because it enables us to choose between 2
    investments when one has a higher expected rate
    of return, but the other has a lower standard
  • It measures the the risk per unit of return.
  • COV Standard Deviation
  • Expected Return

Measuring Stand-Alone Risk
  • Entails determining
  • the uncertainty inherent in the projects cash
  • the nature of the individual cash flow
    distributions and their correlations with each
    other to determine the nature of the NPV
    probability distribution.

Probability Density
Flatter distribution, larger ?,
larger stand-alone risk.
0 E(NPV)
Corporate Risk
  • The risk that the project contributes to the firm
    as a whole (the effect of the project on the
    earnings and cash flow variability of the firm).
  • Corporate risk considers the fact that some of
    the project's risk will be diversified away
    when the project is combined with the firms
    other projects.
  • However, corporate risk ignores shareholder
  • Depends on the projects ?, and its correlation
    with returns on the firms other projects.
  • Measured by the projects beta.

Project X
Total Firm
Rest of Firm
1. Project X is negatively correlated to
firms other assets. 2. If r lt 1.0, some
diversification benefits. 3. If r 1.0, no
diversification effects.
Market Risk
  • The effect (risk) of the project on a well
    diversified stock portfolio.
  • It takes in consideration the stockholders other
    assets (investments).
  • Depends on projects ? and its correlation with
    the stock market.
  • Measured by the projects market beta.

Variables that Influence a Projects NPV and IRR
  • Market Size
  • Selling Price
  • Market Growth Rate
  • Market Share (unit volume sales)
  • Residual Value of Investment
  • Operating/Fixed Costs
  • Investment required

Sensitivity Analysis
  • Answers the question what if
  • Shows how changes in one variable affects NPV or
  • The value of one variable is changed while
    holding all other variables constant.
  • Provides some idea of stand-alone risk.
  • Provides breakeven information.

Why is sensitivity analysis useful?
  • Provides some idea of stand-alone risk.
  • Identifies dangerous variables.
  • Provides breakeven information.

Sensitivity Analysis
  • Each variable is changed by several percentage
    points above and below its expected value (while
    holding the other variables constant).
  • Then a new NPV is calculated using each of these
  • Finally the set of NPVs is plotted against the
    variable that was changed.

Change from Base Level Change from Base Level Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s)
Change from Base Level Change from Base Level Unit Sales Unit Sales Salvage Salvage k
-30 10 78 105
-20 35 80 97
-10 58 81 89
0 82 82 82
10 105 83 74
20 129 84 67
30 153 85 61
NPV (000s)
Unit Sales
-30 -20 -10 Base 10 20
30 Value
Sensitivity Analysis
  • Slope of the lines in the graphs show how
    sensitive NPV is to changes in each of the
  • The steeper the slope, the more sensitive the NPV
    is to a change in the variable.
  • Comparison of 2 projects - the one with the
    steeper slope (sensitivity lines) would be
    riskier, because for that project a relatively
    small error in estimating a variable would
    produce a large change in the projects expected

Results of Sensitivity Analysis
  • Steeper sensitivity lines show greater risk.
    Small changes result in large declines in NPV.
  • Unit sales line is steeper than salvage value or
    k, so for this project, should worry most about
    accuracy of sales forecast.

Weaknesses ofSensitivity analysis
  • Does not reflect diversification.
  • Says nothing about the likelihood of change in a
    variable, i.e. a steep sales line is not a
    problem if sales arent expected to fall.
  • Ignores the relationships among variables.

Scenario Analysis
  • Considers both the sensitivity of NPV to changes
    in key variables and identifies the range of
    possible outcomes under the worst, best, and most
    likely case.
  • It considers the impact of simultaneous changes
    in key variables on the project.
  • It provides a range of possible outcomes.

Scenario Analysis
  • Standard Deviation of NPV
  • Coefficient of Variation

Scenario Analysis
  • The projects COV can be compared with the COV of
    the companys average project to get an idea of
    the relative riskiness of the project under
  • Although scenario analyze can provide useful
    information about a projects stand alone risk,
    it is limited because it only considers a few
    discrete outcomes (NPVs), even though there can
    be an infinite amount of possibilities.

Assume all variables are known with certainty
except unit sales, which could range from 900 to
Scenario Probability NPV(000)
Worst 0.25 15
Base 0.50 82
Best 0.25 148
E(NPV) 82 ?(NPV) 47 CV(NPV)
?(NPV)/E(NPV) 0.57
If the firms average project has a CV of 0.2 to
0.4, is this a high-risk project? What type of
risk is being measured?
  • Since CV 0.57 gt 0.4, this project has high
  • CV measures a projects stand-alone risk. It
    does not reflect firm or stockholder

Would a project in a firms core business likely
be highly correlated with the firms other assets?
  • Yes. Economy and customer demand would affect
    all core products.
  • But each product would be more or less
    successful, so correlation lt 1.0.
  • Core projects probably have correlations within a
    range of 0.5 to 0.9.

How do correlation and ? affect a projects
contribution to corporate risk?
  • If ?P is relatively high, then projects
    corporate risk will be high unless
    diversification benefits are significant.
  • If project cash flows are highly correlated with
    the firms aggregate cash flows, then the
    projects corporate risk will be high if ?P is

Would correlation with the economy affect market
  • Yes.
  • High correlation increases market risk (beta).
  • Low correlation lowers it.

Subjective risk factors should also be considered
  • A numerical analysis may not capture all of the
    risk factors inherent in the project.
  • For example, if the project has the potential for
    bringing on harmful lawsuits, then it might be
    riskier than a standard analysis would indicate.

Weaknesses of Scenario Analysis
  • Only considers a few possible out-comes.
  • Assumes that inputs are perfectly correlated--all
    bad values occur together and all good values
    occur together.
  • Focuses on stand-alone risk, although subjective
    adjustments can be made.

Monte Carlo Simulation
  • A computerized version of scenario analysis.
  • Computer randomly selects a value for each
    variable and combines these values to determine
    the NPV/IRR of the project.
  • The process is repeated many times (1,000 or
    more) until a probability distribution of the
    projects NPVs/IRRs is developed with its own
    expected value and standard deviation.

Monte Carlo Simulation
  • The inputs to a simulation include all of the
    principal factors affecting the projects
    profitability, and the simulation output is a
    probability distribution of NPVs or IRRs for the
  • The project is accepted if the decision maker
    feels that enough of the distribution lies above
    the normal cutoff criteria (NPV gt0) or (IRRgt
    Required Rate of Return).

Simulation Results (1000 trials)
  • Units Price NPV
  • Mean 1260 202 95,914
  • St. Dev. 201 18 59,875
  • CV 0.62
  • Max 1883 248 353,238
  • Min 685 163 (45,713)
  • Prob NPVgt0 97

Interpreting the Results
  • Inputs are consistent with specified
  • Units Mean 1260, St. Dev. 201.
  • Price Min 163, Mean 202, Max 248.
  • Mean NPV 95,914. Low probability of negative
    NPV (100 - 97 3).

Histogram of Results
Probability Density
x x x x x x x x x x x x x x x x x x x x x x x x
x x x x
x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x
Also gives ?NPV, CVNPV, probability of NPV gt 0.
Advantages of Monte Carlo Simulation
  • Reflects the probability distributions of each
  • Shows range of NPVs, the expected NPV, ?NPV, and
  • Gives an intuitive graph of the risk situation.

Weaknesses of simulation
  • Difficult to specify probability distributions
    and correlations.
  • If inputs are bad, output will be badGarbage
    in, garbage out.

Project Risk Analysis
  • Sensitivity, scenario, and simulation analyses do
    not provide a decision rule. They do not
    indicate whether a projects expected return is
    sufficient to compensate for its risk.
  • Sensitivity, scenario, and simulation analyses
    also ignore diversification. As a result, they
    measure only stand-alone risk, which may not be
    the most relevant risk in capital budgeting.

Risk Adjusted Discount Rate
  • Calculate the NPV of a project, using a discount
    rate that has been adjusted for the riskiness of
    the project.
  • Risk premiums applied to individual projects are
    chosen in a subjective manner.
  • Projects assigned to risk classes and then the
    same discount rate is assigned to all projects in
    each class.

Cost of Capital
  • Capital amount of money raised by a corporation
    from creditors and investors through the issuance
    of bonds (debt), preferred stock, and/or common
  • Cost the rate of return required by investors
    and creditors who supply capital to the firm, or
  • The cost to the corporation of raising funds from
    investors and/or creditors, or
  • The minimum rate of return required on new
    investments undertaken by the firm.

Capital Structure
  • The proportion of a firms total assets financed
    by debt, preferred stock, and common stock.
  • Component cost - the required rate of return on
    each source of capital (debt, preferred stock,
    common stock)
  • Target Capital Structure - percentages are set
    for different financing sources.

Weighted Average Cost of Capital (WACC)
  • The average (after-tax) cost of the sources of
    capital weighted by the proportion of each
    component in the firms capital structure.
  • EVA - firms create value if their income exceeds
    the cost of capital used to finance their
  • For a project to be accepted, it must generate a
    return greater than its WACC.

  • The WACC is based on the weighted costs of the
    individual components of capital. The weights
    are equal to the proportion of each of the
    components in the target capital structure.
  • The appropriate component costs to use are the
    marginal costs or the costs associated with the
    next dollar of capital to be raised. These may
    differ from the historical costs of capital
    raised in the past.

Marginal Cost of Capital
  • The primary objective of managers is to maximize
    shareholder value. To do this managers must
    select projects that are expected to earn more
    than the firms cost of capital.
  • To evaluate a project that requires raising and
    investing new capital, managers must compare the
    marginal cost of capital to the projects
    expected return.

Cost of Debt
  • The after-tax cost of debt is used in the
    calculation of WACC because of the tax savings
    that result from the deductibility of interest.
  • kd ( 1- Tax rate)

Component Cost of Debt
  • Interest is tax deductible, so the after tax (AT)
    cost of debt is
  • rd AT rd BT(1 - T)
  • 10(1 - 0.40) 6.
  • Use the nominal rate.

Cost of Preferred Stock
  • The rate of return investors require on the
    firms preferred stock adjusted for flotation
  • kps Dps/Pn
  • Because of the non-deductibility of preferred
    stock dividends, the cost of preferred stock is
    higher than that of debt. As a result, firms
    prefer to issue debt rather than from preferred

Cost of Preferred Stock
  • PP 113.10 10Q Par 100 F 2

Use this formula
Picture of Preferred Stock
rps ?
Cost of Common Stock (ks)
  • The rate of return required by investors in the
    firms common stock.
  • Equity capital can be raised internally through
    retained earnings or through the sale of new
  • The cost of retained earnings is the opportunity
    cost, i.e. the return that investments could earn
    in alternative investments.

Cost of Common Stock (ks)
  • Funds generated through earnings can either be
    paid out as dividends or retained to be reinvest
    them in the firm.
  • If the funds are paid out as dividends,
    stockholders can reinvest these dividends
    elsewhere to earn an appropriate rate of return.
  • The cost of internal equity to the firm is less
    than the cost of new common stock, because the
    sale of new stock requires the payment of
    flotation costs.

Two ways to determine the cost of equity, ks
1. Capital Asset Pricing Model ks kRF (kM -
kRF)b kRF (RPM)b. 2. Dividend Growth Model ks
D1/P0 g
Capital Asset Pricing Model
  • The rate of return investors require on the
    firms common stock is a function of the risk
    free rate (kRF Treasury Bond rate), the market
    risk premium, and the firms beta.
  • rs rRF (RPM )bi
  • Equity/Market Risk Premium RPM (rM - kRF)
  • The additional return that investors require to
    invest in risky equities.

Estimating Beta
  • Run a regression with returns of the stock in
    question plotted on the Y axis and returns on the
    market portfolio plotted on the X axis.
  • Historical beta based on the past relationship
    between a stocks return and the returns of the
    market portfolio.

Cost of equity based on the CAPM
  • rRF 7, RPM 6, b 1.2
  • rs rRF (rM - rRF )b.
  • 7.0 (6.0)1.2 14.2.

Dividend Growth Model
  • ks D1/P0 g
  • D1 - dividend to be paid next year
  • P0 - current price of the stock
  • g - expected growth rate of dividends
  • g (Retention Rate)(ROE) or
  • g (1- Payout Ratio)(ROE)

Dividend Growth Model
  • Future dividends are assumed to grow at a
    constant rate.
  • Payout ratio - the proportion of earnings (net
    income) paid out in the form of dividends.
  • Retention rate - the proportion of earnings not
    paid out as dividends (i.e. retained and
    reinvested in the firm).

Whats the DCF cost of equity, rs?Given D0
4.19P0 50 g 5.
Weighted Average Cost of Capital
  • WACC wdkd(1-T) wpskps wceks
  • Represents the average cost of each new or
    marginal dollar of capital supplied.
  • Percentage capital components (wd, wps, wce) are
    based on accounting book values, current market
    values of the components, or the targeted capital

Determining WACC
  • 1) Calculate the cost of capital for each
    individual component.
  • kd ( 1- Tax rate),
  • kps Dps/Pn
  • ks D1/P0 g
  • 2) Compute the weighted (marginal) cost of
    capital for each increment of capital raised.

Factors Affecting WACC
  • Interest Rates
  • Market Risk Premium
  • Tax Rates
  • Capital Structure Policy
  • Dividend Policy
  • Investment Policy

Estimating Project Risk
  • The (marginal) cost of capital is a function of
    projects risk.
  • The firms WACC is closely related to the degree
    of risk associated with new investments, existing
    assets, and the firms capital structure.
  • The 3 risks associated with a project are
  • Stand-alone risk
  • Corporate or with-in firm risk
  • Market or beta risk

Divisional Beta
  • Security Market Line - expresses the risk return
  • ks kRF (kM - kRF)bi
  • bi - the beta of a division.
  • ks - required rate of return on the divisions
  • investment.

Estimating Project Risk
  • Stand Alone risk - the projects diversifiable
    risk. It is measured by the variability of the
    projects expected returns.
  • Corporate/Within Firm Risk - the projects
    contribution to the firms overall risk (the fact
    that the project represents only one of the
    firms portfolio of assets. It is measured by the
    projects impact on uncertainty about the firms
    future earnings.

Estimating Project Risk
  • Market/Beta Risk - project's risk as viewed by
    the a well diversified stockholder who recognizes
    that the project is only one of the firms assets
    and that the firms tock is but one part of the
    investors total portfolio.
  • Measures by the projects impact on the firms
  • Market Risk directly affects the stock prices.

CAPM and Project Risk
  • Using the CAPM to estimate a projects risk
    adjusted cost of capital
  • kproject kRF (kM - kRF)bproject

Capital Asset Pricing Model
  • Market (systematic) risk is the only relevant
    risk for capital budgeting purposes.
  • Firm can be viewed as a portfolio of assets, each
    having its own beta.
  • The beta of a firm is the weighted average betas
    of its individual assets.

Mistakes in Estimating WACC
  • Using the current cost of debt instead of the
    interest rate on new debt.
  • Using the historical average rate return on
    stocks instead of the current expected rate of
    return on stocks to estimate the risk premium.
  • If the targeted capital structure is unknown use
    the market values to obtain the weights.
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